I have the opposite problem with mine. It goes down when reverse is selected but then forgets to go back up sometimes..  Bushy

2003 RR Vogue Monté Carlo Blue

Still didn't work for me. I have full movement on both mirrors, up-down-in-out, just don't seem to memorize the settings.

iphs sounds exactly the same as my issue perhaps something is required on the diagnostics - Definitely no issue with motors etc as far as I can see  Now: BMW 640d M Sport, Alpine White
Gone: Range Rover 4.4 V8 Vogue, Zambezi Silver, Charcoal Oxford Leather
Also: Mk1 Audi TT 1.8T Quattro, Brilliant Black
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There's a couple of things you could try.

The drivers door mirror can also be set in different positions and the positions stored on the memory buttons M1, M2 and M3.
Set the drivers door mirror and store the position in the memory as above.
Then physically move the mirror to a different position using the door controls.
Press M1 with the ignition on and the mirror should drive to the stored position.
This would show whether or not the memory function works at all.

Next is a battery disconnect and reconnect and then try setting the reverse function again.

Lastly the car needs plugged into a diagnostic system to check if a fault is logged in the Body Control Module.

If the mirrors cannot be made to work then I have no idea, sorry.